应用数学2016，Vol.29Issue(1)：152-160,9.
Hilbert格上的极小不动点定理及其在不连续变分不等式中的应用
Minimal Fixed Point Theorem and its Applications to Discontinuous Variational Inequalities in Hilbert Lattices
摘要
Abstract
In this paper,we use the dual version of Zorn's lemma to obtain a minimal fixed point theorem for lower order-preserving set-valued mappings in Hilbert lattices.Applying this fixed point theorem,we introduce an existence theorem of minimal solutions to generalized variational inequalities.Furthermore,we also study the lower order-preservation of solution correspondence for parametric generalized variational inequalities.In contrast to many papers on variational inequalities,our approach is order-theoretic and the results obtained in this paper do not involve any topological continuity with respect to the considered mappings.关键词
极小不动点/保序性/Hilbert格/广义变分不等式Key words
Minimal fixed point/Order-preservation/Hilbert lattices/Generalized variational inequality分类
数理科学引用本文复制引用
王月虎,刘保庆..Hilbert格上的极小不动点定理及其在不连续变分不等式中的应用[J].应用数学,2016,29(1):152-160,9.基金项目
Supported by the National Natural Science Foundation of China (11071109,11401296),the Jiangsu Provincial Natural Science Foundation of China (BK20141008) and the Natural Science Fund for Colleges and Universities in Jiangsu Province (14KJBl10007) （11071109,11401296）
